06 December, 2012

EDIT: Portions of this article when first published were factually inaccurate. These errors have since been corrected using strikethrough text.

Occasionally, when I'm talking to younger people and they find out that I'm mathematically literate, I'll get a question of the form: "What's the biggest number you can name?"

It's a somewhat difficult question to answer, because it really depends on what counts as naming and what counts as a number. After all, am I allowed to use a function to identify a number? Does the number have to be finite? Must it be useful in some sense? Should I include transfinite numbers? Or do they just want the highest number that has a common english name?

Since there are different answers depending on what the questioner thinks is acceptable, I'll try to list a few of the standard answers I give to these younger questioners here, starting from the smallest and work my way up. If I've missed any natural answers to the question, please comment with your suggestion, so I can add it to my repertoire.

Common English Names

The first few counting numbers have names that we commonly use in English, e.g., ten, hundred, thousand, million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, &c. Some of these get obscure, but they're nevertheless understandable. One of the largest of these in fact has a famous search engine named after it: a googol is equivalent to 10^100. Google's headquarters is also named after an even larger such number; the Googleplex near San Jose, California, is named after the googolplex, which is 10^(googol). In between these two values is the centillion at 10^303, which is about as large as you can get while using the "-illion" suffix. (You can artificially construct larger terms, like the uncentillion, but this is just a matter of inserting additional prefixes.)

Of note here should be Archimedes' system of estimating the number of grains of sand that could fill the universe at 10^63 by using a unit called the myriad, which is equal to 10,000. Archimedes did this by calling a myriad of myriads the first unit, and then taking a myriad myriad of myriad myriad units to create the second unit, and so on for eight times, saying this would be sufficient to fill the universe with grains of sand.

Mathematical Notation

Of course, there are many numbers that are much larger than these, but they generally do not have common english names. Rather, we write them out using scientific notation or by some other mathematical notation. The googolplex above is only 10^(10^100); if you want something bigger, you need only write out another exponent. But even if you repeatedly take exponents of exponents all day long, you won't get anywhere near where you can get if you instead use a more efficient notation system.

Mathematical operations build upon themselves recursively, as any schoolchild learns when they begin to see the relationship between addition and multiplication. Exponentiation is the next logical step after multiplication, but there are further steps one can take. The next method up is called tetration, and it involves repeated exponentiation.

The addition of A+N is when you take the number A and succeed it N times. The multiplication of A*N (or A×N) is when you take A and add it to itself N times. The exponentiation of A^N (or AN) is when you take A and multiple it to itself N times. The tetration of NA is when you take A and exponentiate it by itself N times. I'm sure you can see the pattern here.

NA is A^A^…^A^A where there are N As in the sequence. This results is very large numbers. 10010 is much bigger than 10100, for example. But some notations go far beyond mere tetration.

One such way of notating large numbers is by using Knuth's up-arrow notation. Rather than use superscript, up arrows are used to indicate which type of operation is being used. Exponentiation is written out as A^N (or A↑N) instead of AN. Tetration is written as A^^N (or A⇈N or A↑2N) instead of NA. And the next step in the series follows the same rule: pentation is written as A^^^N (or A↑↑↑N or A↑3N), which is just taking A and tetrating it N times. Similarly, hexation is A^^^^N (or A⇈⇈N or A↑4N), which is taking A and pentating it N times. And so on.

It is perhaps a little difficult to fully understand the scale of these numbers. Even the innocuous looking 3^^^3 is much, much, much bigger than a googolplex:

Add another arrow or two in there and the number becomes so large that trying to just think about it boggles the mind. Usually, when I want to name a very large finite number, I will go with 3^^^^3. It's far bigger than almost anything that we deal with in reality, and so effectively works as a stand in for "extraordinarily large finite number".

However, it's not even close to the biggest that some mathematicians work with.

Graham's number refers to the number of dimensions a hypercube must have in order to satisfy some esoteric conditions in Ramsey theory. The number is so large that the number of up-arrows you'd need to display it is itself amazingly huge. Here's a lower bound of Graham's number: Here's one upper bound of Graham's number that isn't even the lowest known upper bound:

In the above equation, notice that the number of up arrows in the first line is indicated by the number in the line below it. My "extraordinarily large finite number" that I commonly use, 3^^^^3, is merely the number of up arrows used in the sequence directly above it. As you can see, Graham's number is huge.

Fast Growing Functions

And yet, Graham's number is not nearly as big as some. If functions are allowable in our answer, then much bigger numbers can be shown in a small amount of space. Unfortunately, many people seem to think that saying f(x) where the function is defined as X+1 is not the same thing as naming a number. If I say f(3), we all know that what I'm pointing at is 4, but perhaps we might say that I only pointed at it and yet did not name it. However, there is philosophical debate on this issue; after all, what more is there to naming than pointing out which thing we mean? In a very real sense, f(3) can be said to be yet another name for the number 4 here. If you agree with this logic, then we can easily construct much bigger numbers than even Graham's number by merely using functions that grow much faster than even nested up arrow notation can handle.

Take the busy beaver function. It refers to the maximum number of steps performed by turing machines of a certain class, and has been mathematically proven to grow faster than any computable function, though there might non-computable functions that grow even faster. It starts out slow, with Σ(12) being only 3^^^^3, the bottom line of Graham's number. But it grows fast, where Σ(2k) > 3↑k-23 > A(k-2,k-2) (k≥2), and A() is Ackermann's function: A(m,n)=2↑m-2(n+3)-3.But if you think the busy beaver function grows quickly, then consider the TREE(x) function. It was created to deal with trees in set theory and grows much faster than most people can appreciate. TREE(3)=A(A(...A(1)...)), where the number of As is A(187196), and A(x) is a version of Ackermann's function: A(x) = 2↑x-1x. Compare to Graham's number, which is just A64(4) — a much smaller number than the established lower bound of TREE(3) at AA(187196)(1). If you want to a compact way of pointing out an absurdly large finite number, consider using TREE(100). The only way I know of to reliably get higher ordinals is to put in bigger numbers inside the function, and god help you if you start iterating the function inside itself.

Take the TREE(x) function. It was created to deal with trees in set theory and grows much faster than most people can appreciate. TREE(3)=A(A(...A(1)...)), where the number of As is A(187196), and A(x) is a version of Ackermann's function: A(x) = 2↑x-1x. Compare to Graham's number, which is just A64(4) — a much smaller number than the established lower bound of TREE(3) at AA(187196)(1). If you want to a compact way of pointing out an absurdly large finite number, consider using TREE(100).

But if you think the TREE() function grows quickly, then consider the busy beaver function. It refers to the maximum number of steps performed by turing machines of a certain class, and has been mathematically proven to grow faster than any computable function, though there might non-computable functions that grow even faster. It starts out slow, with Σ(12) being only 3^^^^3, the bottom line of Graham's number. But it grows fast, where Σ(2k) is

and A() is Ackermann's function: A(m,n)=2↑m-2(n+3)-3. The only way I know of to reliably get higher ordinals is to put in bigger numbers inside the function, and god help you if you start iterating the function inside itself.

Edit: This section was originally inverted, and incorrectly portrayed the TREE() function as faster growing than the Busy Beaver function.

Infinity and Beyond

Of course, all the above numbers are finite, so there is at least one number that beats them all: ∞. Yet the infinity that most people think of when they imagine "the infinite" is merely א0, the first and lowest transfinite cardinal number. These are countably infinite sets, like the set of all positive integers. Yet this comparatively small infinity dwarfs in comparison to א1, the uncountable set which might correspond to the cardinality of real numbers. (This the continuum hypothesis, and it only works if 2^(א0)=א1, which is far from clear.)

But cardinality is not the only kind of infinity; there are also ordinal infinities. The lowest transfinite ordinal number is ω, which corresponds to the order type of the natural numbers. We can then consider the אa where a=ω. This makes אω, which is the lowest uncountable cardinal number that is not the same as the cardinality of the real numbers. the smallest uncountable cardinal provably in ZFC that is not the cardinality of ℜ. (The cardinality of the real numbers might be א1, which is smaller, or אω+1, which is bigger (or many other cardinals).) Don't worry if this is starting to make you dizzy; it does the same to me, too.

However, this is just the low end of the scale. At the high end, things really get deep. Dedekind looked at the system of all ordinal numbers, calling it Ω. Wondering if he could get even higher, he proposed the sequence:

{0, 1, 2, 3, … ω0, ω0+1, …, γ, …}

where each γ in the sequence goes on to describe the order type of all preceding elements. But this turns out to be inconsistent, since if it were consistent, then there would be some number that corresponds to its order, and that number would have to be higher than any of the numbers in the above sequence. But since this is a number, it must be in Ω to begin with, since Ω has all numbers in it. But a number cannot be greater than itself, and so this new proposed set by Dedekind cannot exist. This means that Ω is definitely the absolute infinity of its class.

Does this mean that Ω is the winner here? Can we get any bigger? The answer, once again, is it depends. Woodin's Ultimate L, LΩ, is the ultimate enlargement of Gödel's constructible universe L, which is itself the proper class of all constructible pure sets. Here, L refers to the standard inner model universe of the inner model theory ZFC+V=L, where ZFC is Zermelo-Fraenkel set theory and V is the Von Neumann Universe stationary club (closed unbounded class) of all well-founded pure sets.

That's a mouthful, but does it mean that is LΩ "higher" than Ω? I don't know that it even makes much sense to ask the question, because they're talking about different things. Yet they're both "numbers", so maybe that means they can be compared anyway? To be honest, I'm not entirely sure. When it comes to infinities any bigger than א0, my brain implodes. The previous paragraph, in fact, was written with only a vague understanding of what I've read elsewhere — it's more regurgitation than true understanding on my part.

Conclusion

After all this, I suppose the biggest entity I feel comfortable talking about is Ω, especially when it comes to trying to answer unexpected questions from younger people. Concepts like Hausdorff's absolute continuum cΩ or Woodin's Ultimate LΩ describe situations that may or may not correspond to אω or Ω or whatever. For all I know, everything from אω and up are all equivalently large entities. At some point I may bother trying to understand this stuff more in depth, but until then I think I'll just stick with the large finite numbers and Ω if they want to know how big ∞ can truly get.

EDIT: A few mathematicians expressed concern that some of the mathematical sentences I originally presented in this essay were factually incorrect. These errors have since been corrected, and previous text has been left in using strikethrough text to illustrate the errors I originally ran into as a layperson attempting to write a mathematical article. Thank you to professor Edgar Bering and grad students Bo Waggoner and Charlie Cunningham for finding and correcting my errors.

15 November, 2012

Ghostwriting for companies, organizations, and people that you don't really believe in is soul-wrenching work. Some of the things I've done for money recently are pieces that I am not at all happy about writing.

When I left as webmaster of one national nonprofit in particular (while it's easy to use Google to find out which, I'll leave them unnamed here for reasons that will become explicit), I had very specific ideas on the kinds of things I wanted to do. I never liked how that organization would use misleading language on the severity of child hunger in America (food insecurity for one day in a year should be prevented, but to call the 1 in 5 statistic for this a "hunger" statistic seems disingenuous to me), and the sheer amount of money it spent on getting high profile celebrities to represent the brand utterly floored me. I was completely flabbergasted when I first saw just how much of people's donations were going toward paying for obscure extravagancies that celebrities insisted on. Yet it's hard to fault them for this behavior, since the celebrities did bring in additional donations that more than made up for the thousands spent on keeping whiny celebs happy. If what matters is getting the most money to spend on the cause, then I suppose they were justified in wasting money on severely overpriced hotel rooms and other shockingly "wasteful" expenditures that celebrities insisted on, such as additional empty hotel rooms next door to theirs. I put "wasteful" here in quotes because, in the end, the organization raised money by catering to such asshole celebrities. So, in a way, these "wasteful" costs were worthwhile. But the fact that these celebrities insisted on spending a child hunger charity's money in this way really made me feel uneasy.

As a consequentialist-style revisionist, I really do feel that outcomes are what matters in the end. So it's hard for me to fault this organization's practices. Their mission is well intentioned, and they do a very good job of raising money for it, but it always felt so slimy when I had to write cop on their website or in their newsletters about the issue of child hunger in America. Every time I made it seem like the issue was more severe than it actually is, I cringed inside. And yet I performed this function for years, drafting language that would best turn into donations instead of language that would best reflect the truth.

After I left, I desperately wanted to work in optimal philanthropy community. I figured I could accomplish some real good if I at least worked in a field that was smart about how it allocated funds. But the job market is tough, and instead I've been ghostwriting ever since. Ironically, I seem to be writing for sleazier and sleazier groups all the time. Maybe it's because I'm good at it, but I suppose it's more likely that I'm just not trying hard enough to do what I really want to do.

[Edit from October 2015: I later came to the field of Effective Altruism mostly due to the negativity experienced at traditional nonprofits discussed in this entry.]

11 November, 2012

As promised in a previous entry, I have decided to make my answers to the 2009 PhilPapers Survey public on my blog. These answers were previously made public in a LessWrong poll, but in the interest of making my specific positions easy to read, I've compiled them all here. Note that this post is intended solely to give my position on each of these issues, and does not currently have commentary on why I feel as I do. However, in future entries I intend to zero in on each issue; as I do so, I plan to link to those entries from these position statements in order to more explicitly share why I hold these particular philosophical positions.

My answers are given in bold. The distribution of answers from the 2009 PhilPapers survey is given as a percentage after each answer. Note that percentages for "accept" and "lean toward" are combined here, although more finely grained results are available on the PhilPapers site. A short explanation (thanks to pragmatist & PhilPapers' clarifications for help) of each question is provided for any readers that are not well versed in these issues. Links to future blog posts on why I hold each position will be made available as I write them. Links to relevant SEP articles are provided.

Omega appears before you with two boxes and says you may take Box A or take both Box A and Box B. Omega has almost certain predictive power and does not lie. Omega has predicted which you will choose; if Omega predicts you will take just Box A, then Box A will contain $1,000,000. Box B always contains $1,000. How many boxes do you take?

Scientific anti-realism: There are no strong reasons to believe in their theoretical claims about unobservable entities (though epistemic justification of predictions exist).

Scientific realism: There are strong reasons to believe in the theoretical claims about unobservable entities made by our best scientific theories.

Teletransporter (new matter): survival or death?

Accept: survival (36.2%)

Lean toward: survival

Accept: death (31.1%)

Lean toward: death

Other (32.7%)

You are placed in a machine that will instantaneously disintegrate your body, in the process recording its exact atomic configuration. This information is then beamed to another machine far away, and in that machine new matter is used to construct a body with the same configuration as yours. Would you consider yourself to have survived the process, and teleported from one machine to the other ("survival")? Or do you think you have died, and the duplicate in the far away machine is a different person ("death")?

There is a trolley traveling along a set of tracks. The driver has lost control of the trolley. On the track ahead of the trolley are five people who cannot get off the track in time and will all die if the trolley gets to them. You are standing next to a lever that can switch the track the trolley will take, preventing the deaths of the five people. On the other track is a single person who also cannot get away in time and so will die if you switch the track. Do you refrain from switching the track or do you switch the track?

Correspondence: A proposition is true if and only if it bears some sort of congruence relation to a state of affairs that obtains.

Deflationary: Ascribing truth to a proposition amounts to no more than asserting the proposition.

Epistemic: To say that a proposition is true is just to say that it meets a high standard of epistemic warrant, and that we are thereby justified in asserting it.

Zombies: inconceivable, conceivable but not metaphysically possible, or metaphysically possible?

Accept: inconceivable (16.0%)

Lean toward: inconceivable

Accept: conceivable but not metaphysically possible (35.6%)

Lean toward: conceivable but not metaphysically possible

Accept: metaphysically possible (23.3%)

Lean toward: metaphysically possible

Other (25.1%)

A zombie is physically identical to a human being but does not possess phenomenal experience. There is nothing it is like to be a zombie.

Inconceivable: We cannot fully conceive of a zombie.

Conceivable but not metaphysically possible: One can arrive at a coherent conception of zombies, but objects that match this conception cannot possibly exist, not even in worlds with different laws of nature than ours.

08 November, 2012

When I was young, I was a fan of The Spark, an online community that revolved around taking tests and quizzes about one's personality. It was silly, but I was serious enough about it to actually stay on the site for years, even after they switched over to OkCupid, which is primarily a dating and friendship finding community site.

While most of those tests are now the kind of thing that I don't take seriously at all, there are quite a few that nonetheless have some minor level of legitimacy to them. As I was taking the 2012 LessWrong Census/Survey, quite a few of these test results were requested, and so I ended up retaking several of the more scientific ones. It seemed wasteful to only allow that information to be used for CFAR, so I thought it might be appropriate to pull together these results here in a blog post. Consolidating this data is probably not worth reading for most of my blog subscribers (feel free to close this page now, all of you), but if you're the Eric of the future who is wanting to compare results from these tests taken years later, this is as good a place as any for me to compile the data.

So, without further ado, I present the results of several personality (and other) tests taken this year.

Big Five (OCEAN)

The Big Five test scores on openness, conscientiousness, extraversion, agreeableness, neuroticism. (Hence why it is sometimes referred to as the OCEAN test.) These personality traits are often used by psychologists as a model of human personality. I took the test at outofservice.com/bigfive. My scores are available there, and reproduced below.

Openness: 96%

Conscientiousness: 96%

Extraversion: 4%

Agreeableness: 87%

Neuroticism: 1%

Political Compass

Political stances differ widely between most people, not just in terms of economic Left and Right, but also in terms of social libertarian/authoritarian values. The test at politicalcompass.org does an exemplary job of tracking one's political views on a two-dimensional grid. My results are available there, as well as below.

Economic: -10.00

Social: -8.62

Intelligence Quotient

First of all, IQ is not really a useful measure. A simple search through the skeptical literature on how IQ tests are used in our society will easily show this. However, it does have the minor legitimate use of determining one thing in particular: the aptitude of the person taking the test in how well they perform on IQ tests. That sounds silly, but hey: at least it's true. The IQ test I took is available at iqtest.dk, and is wholly pattern oriented, with all cultural questions removed. I scored 122, which is about twenty points less than the score I received in independent testing during my childhood. I'm not sure if this rather dramatic drop says something about the earlier test, this test, or specifically about me.

Myers-Briggs Type Indicator

Jungian typological theories are underneath the MBTI questionnaire, and break down the personality in terms of sensation, intuition, feeling, and thinking. The validity of this test is about on par with IQ; it is currently used, but the evidence for it being useful is lackluster in comparison to how often the test is given. Nevertheless, mainstream opinion seems to be neutral, as opposed to for or against, so it is included here as well. I took the test at Humanmetrics Jung typology test, and received an INTJ classification.

Strong preference of Introversion over Extraversion (78%)

Strong preference of Intuition over Sensing (100%)

Moderate preference of Thinking over Feeling (25%)

Moderate preference of Judging over Perceiving (44%)

Hare Psychopathy Checklist (PCL-R)

While all of the above tests were taken in early November of 2012, the results of the PCL-R I record here come from a self-test administered in May of 2012. The PCL-R is a checklist for sociopathic tendencies, and has both adherents and critics in the field, making it unclear as to how seriously one should take the results. The vast majority of people score a 3 or less on the test; sociopaths generally score 25+. I scored 8. Among all friends that I've talked into taking the test, I am by far the highest. (The highest any of my friends has so far scored is 3.) I'm not sure what this says about any sociopathic tendencies I may or may not have, though I should take pains to assure readers that most people consider me to be a very moral person in general.

Final Notes

If for some reason someone is still reading who isn't me in the future, then you might possibly be interested in knowing where you can find more data from tests I've taken or questions I've answered. I will direct such people to my OkCupid profile, which has well over a thousand questions published that I've answered publicly. While OKC is branded as a dating site, the sheer amount of public data there on questions ranging from personality to morality, everyday outlook to political persuasion, and even metaphysical philosophy to aesthetic tastes can be useful for any number of non-relationship purposes. Also related is my Combosaurus account, which has several additional data points. Combosaurus is currently in alpha, so may not be visible to most people yet. They're run by the same engineers behind The Spark and OkCupid.

Also of interest may be my responses to the PhilPapers Survey of philosophers, which lists just about every philosophical position I have on mainstream philosophical questions.

25 October, 2012

As I did earlier in my blog entry on my favorite podcasts, I present here a list of all tv shows that I watch on a regular basis. Some of these I strongly recommend everyone watch; others I am less certain of making a serious recommendation, even though I honestly watch every episode that comes out.

Note that every show on this page is one I watch every time a new episode comes out, so all are shows I obviously consider good. But some are nonetheless better than others. Shows that I strongly recommend are in bold.

How to Use This List

Each show title is linked to its page on ShowRSS for ease of subscribing (except where torrent rss feeds are unavailable or where shows have ended). I highly recommend using ShowRSS; their service automates downloading of new episode torrents (from EZTV) of your favorite shows. Note that setup will require software to take the rss feed from ShowRSS and plug it into your BitTorrent client. (I use Catch and µtorrent respectively. Catch is Mac only; PC users can use Miro instead, though I can't personally vouch for how well it works.)

Where the show is no longer getting new episodes, I've instead linked to a magnet torrent TPB page for the complete series instead. (Be aware that for long series, this will be a BIG download. Use manual searches if you need smaller download chunks.) In the rare case where new episodes are still being made but ShowRSS does not have a feed (this happens when EZTV does not release a torrent rss), I will link to the most relevant page I'm aware of that can direct you to new episodes.

Remember that subscribing to a ShowRSS feed will not get you old episodes. You still need to manually download past episodes to catch up first. If you have any problems, remember that you can always do a manual search on The Pirate Bay.

(Please note that most anime are better subbed than dubbed. Seriously. Some of the anime I recommend below have really bad vocal English tracks. Exceptions are explicit.)

Situational Comedy

The Big Bang Theory: A mix of really bad comedy with very good comedy. This feels a bit like SNL in that there are really good parts and really, really bad parts even though BBT is scripted and has no "live" excuse.

30 Rock: Strong meta-situational comedy. Watch more than a couple of episodes before giving up on this; it takes a while for viewers to realize just how good some of this writing is.

Science Fiction

Cowboy Bebop: More western sci-fi awesomeness. Link is to dual audio. Excellent English voice actors.

Babylon 5: Well-rounded sci-fi epic. Has a bit of each genre and is clearly a part of '90s culture, but has themes which overcome these initial hurdles.

Battlestar Galactica: The dramatic remake of BSG is what most current scifi shows consider as the standard dark scifi series. (Compare to ST:TNG, the "standard" light scifi series.) Spinoff Caprica will be of interest to fans.

Stargate Universe: While I enjoyed the previous Stargate series more than the average guy, SGU is a clear standout in the Stargate universe (pun intended). This is worth watching even if you're unfamiliar with Stargate canon in general.

Star Trek: Every series (tos, tng, ds9, voy, ent) is well worth watching. Quality of individual episodes does vary, but the cultural value of seeing the best of them is worthwhile.

Farscape: Fair warning: this takes a long time to get into. A full appreciation requires an attention to detail that most shows do not demand of viewers.

Stargate: Note that Stargate Universe is a bold recommendation above. Other entrants in this series (SG1, SGA) are worth watching, but not at the level of SGU.

Doctor Who: Classic sci-fi. Not the best on a show-by-show basis, but worth watching for the long-term lore and cultural appeal. If you're new to the series, start with the ninth doctor (the 2005 series 1) and only watch the older episodes if you become obsessed (as many do). Spinoff Torchwood is terrible, but still of interest to fans.

Fantasy

My Little Pony: Friendship is Magic: Yes, I'm serious. MLP reeks of cuteness and every episode warms my heart. No other show can cheer me up as fast as this. Link is to an r/mylittlepony post that is kept well-updated.

The Vision of Escaflowne: Perhaps the best anime series of all time. Worth watching even if you've never had any interest in anime before. Link is to dual audio.

Neon Genesis Evangelion: An anime classic. Philosophical, topical, yet clearly aimed at a young audience. Worth watching just for the cultural value of being familiar with it alone. Link is to dual audio.

FLCL: An extreme example of parody taken seriously. On one view, this is a commentary on the state of anime post-evangelion; but at a deeper level, this parodies the art of parody itself by turning what would be a mockery into an actual good story on its own merits. I had to watch this short series multiple times before I fully appreciated most of the concepts it had to offer. Link is to dual audio.

I should also mention that there are a few shows that I enjoy that are not listed here, whether it is because it's been so long since they ended that I've forgotten they exist or because they only just started and I'm undecided on if I really like them or not (like Elementary). As time passes, I'll try to go back and edit this post to add shows I neglected on my first draft.

23 October, 2012

I subscribe to a lot of podcasts. I use podcasts to keep up with the news, learn more about the world, and expand my mind generally. As such, I've sampled and stopped listening to more podcasts than most people have even heard of. According to some of my friends, this makes me a fairly good judge of which podcasts are worth investing a bit of time in. Thus, I decided to start maintaining this list of my favorite podcasts.

Strong recommendations are in bold, and should be seriously considered. Non-bold recommendations are good enough to cause me to download and listen to every episode they release, but maybe do not quite stand out enough for me to give a full recommendation. All podcasts recommended on this page are rated five stars by me on itunes; the distinction between bold and non-bold recommendations is slight at best.

Note that I am a man of very specific tastes. I adore philosophy and I have a strong tendency toward rationalism, skepticism, and mathematical rigor. This certainly affects what I consider to be a worthwhile podcast to subscribe to. YMMV.

The Best Philosophy Podcasts

The field of philosophy is blessed to have so many exceedingly good podcasts available to choose from. Some are short bite-sized chunks while others go moderately in-depth on philosophical topics. For serious users, there are even a few excellent full course podcasts available on iTunes University; listening to such a series takes many, many hours, but it can be well worth the time investment if you're fully interested in the topic.

Morality in the Real World (itunes, site): 20 minute sporadic episodes on desirism by Alonzo Fyfe and Luke Muehlhauser. Shows the thinking process of specifically explicating a theory over time, making changes along the way. (Note that desirism is not a theory I subscribe to.)

The Big Ideas (itunes): 10 minute sporadic mini-introductions on the main ideas in philosophy.

Medium-form philosophy podcasts:

The History of Philosophy Without Any Gaps (itunes, blog): 20-30 minute weekly discussions on the history of philosophy by Peter Adamson.

The Partially Examined Life (itunes, blog/forum): 2 hour weekly discussions on philosophical readings aimed at a moderately informed audience. Their forum includes reading groups where listeners can discuss topics more in-depth, which is perhaps the most awesome thing ever.

Why? Philosophical Discussions About Everyday Life (itunes, site): 1 hour bi-weekly interviews on philosophical topics with Jack Russell Weinstein. The host is very good at asking great questions of guests that cut to the heart of philosophical positions.

Philosophy Talk (site/forum): 1 hour weekly discussion on philosophical topics with a call-in audience. Their podcast feed goes through iAmplify, which is terribly confusing and irritating, but each week's episodes are free to download if you can figure it out. Be aware that past episodes are not freely available, making this show impossible to use with philosophy discussion groups.

New Books in Philosophy (itunes): 1 hour biweekly interviews with authors about their newly published books on philosophy. These are easily the most dense of all podcasts listed here, as they go fairly in-depth on specific topics — but every episode is accessible to a moderately well-informed philosophical audience. Unfortunately, the audio quality is not ideal.

Such That Cast (itunes, site): 1 hour monthly interviews with philosophers. Does not focus on specific philosophical problems, but just consists of a freeform conversation between the interviewer and interviewee. This sounds terrible, but is actually really good.

The Best News Podcasts

I don't always agree with the viewpoints expressed on the following programs, but I listen to all of them regularly. I feel it's important to expose oneself to alternate viewpoints on a regular basis as a method of keeping one's political bias in check.

Straight news:

Democracy Now! (itunes video or audio, site/blog): 1 hour daily news program that gives proper air time to voices on the far left. Amy Goodman often raises issues most news sources do not.

NPR News Summary (itunes): 5 minute daily morning news summary. This is easily the best source of headlines each day.

NPR Story of the Day (itunes): 3-10 minute daily stories on various topics. The best story of the day is usually interesting, though you never know what it will be about in advance.

C-SPAN Podcast of the Week (itunes): 1 hour broadcast of the best event that week on C-SPAN. Topics vary widely but are always worth the download.

C-SPAN Newsmakers (itunes): 30 minute interviews with people currently in mainstream political news stories.

Frontline (itunes): This is perhaps the best in-depth news reporting available today. They consistently put out great investigative news stories.

This Week (itunes): 45 minutes weekly political discussion with George Stephanopoulos. They're consistently late on putting these out, but the content is worth it.

Fox News Sunday (itunes): 45 minutes weekly political discussion with Chris Wallace. Despite Fox's deserved reputation for lying, Wallace does an almost respectable job of asking tough questions to those on the right.

Meet the Press (itunes): 45 minutes weekly political discussion with David Gregory. They're consistently late on publishing each episode, and past episodes are not available for download.

State of the Union (itunes): 45 minutes weekly political discussion with Candy Crowley.

Note that I do not approve of the Face the Nation podcast and cannot recommend that anyone subscribe to it. Each episode is one hour long, with a full third of it being nothing but commercials. Of the 40 minutes of content, some 5-10 minutes is wasted on sports commentary rather than political discussion. Listening to this show might be worthwhile if you watch it live on tv, but in podcast form, it is completely unbearable.

The Best Science Podcasts

I adore science. If you do, too, then you'll enjoy these excellent podcasts.

Freakonomics (itunes): 30-45 minute weekly episodes on unusual economic topics. Some 5-minute weekly mini-segments are also in this feed.

Brain Science Podcast (itunes): 1 hour monthly interviews on recent discoveries in neuroscience and how they relate to our philosophy of mind. These can get pretty technical at times.

The Best Skepticism Podcasts

The skeptic community has a lot of podcasts out there, but unfortunately the quality is a bit lacking in many of them.

You Are Not So Smart (itunes): 1 hour monthly interviews on rationality. This is one of the best skeptic podcasts currently being made. Far too many skeptic podcasts are aimed at dealing with absolutely ridiculous claims like bigfoot, ghosts, or homeopathy; but the YANSS podcast deals with dubious claims that even established skeptics may still fall for.

Consequence (itunes): 30-45 minutes biweekly interviews with people harmed by pseudoscientific claims. These are first-hand accounts of the harm caused by belief in false things.

Conversations from the Pale Blue Dot (itunes): 1 hour sporadic interviews with Christians and atheists on the divide between the two.

In any list of the "best" skeptic podcasts, there must be at least some mention of Skeptoid and Skepticality, due to their wide popularity among skeptics. Neither has made my list.

Skeptoid focuses on stories about false claims. It feels like a podcast that tells ghost stories and little more. Meanwhile, Skepticality has some great segments at the beginning of each episode, but the main part of the podcast is just terrible. I reallydislike the main host. His voice is not appropriate for radio, and his interview style is more hurtful than helpful in learning about guests' positions. Not as important (but notable enough to mention) is the very, very, very bad theme song. Seriously, Skepticality has perhaps the worst theme song of any popular podcast I've ever heard.

The Best History Podcasts

I wasn't very interested in history as a child; I was more of a science and math person. That's why these podcasts are so very exciting to me — my prior lack of knowledge in the field means I always learn something new in every episode. Your experience might be different if you're already well versed in these topics.

The History of Philosophy Without Any Gaps (itunes, blog): 20-30 minute weekly discussions on the history of philosophy by Peter Adamson. Perhaps it's unfair that I've listed this podcast twice in two different categories, but it's just that good.

In Our Time (itunes, site): 20-30 minute weekly episodes on the history of ideas by Melvyn Bragg.

The History of Rome (itunes): 30 minute episodes on the complete story of the Roman empire from beginning to end. This podcast series is complete, with no newly published episodes.

The History of Byzantium (itunes): 30 minute weekly podcasts on the history of the Byzantine empire. This series starts where the History of Rome podcasts ends; I strongly recommend listening to the History of Rome series first.

A Brief History of Mathematics (itunes): 15 minute short introductions on the history of mathematics. Series is complete with no new episodes.

Other Podcasts I Enjoy

Not everything I listen to is easily categorized, but I still recommend them just as strongly.

This American Life (itunes): 1 hour weekly episodes on various topics. If you only subscribe to one podcast recommended on this page, let it be this one.

Harry Potter and the Methods of Rationality (itunes): 25 minute weekly audiobook episodes of Eliezer Yudkowski's fanfiction epic. I know the idea of fanfiction may sound silly at first, but this will blow your mind.

The Dice Tower (itunes): Hour long weekly episodes on board game reviews.

Flack Check (youtube): 1 minute daily episodes showcasing the lies politicians tell with an element of humor. Link is to youtube because their itunes feed is not out yet.

Final Notes

Obviously, I consume a lot of content. When you add to this list the other media I regularly consume like television shows and movies, it becomes obvious that I spend a LOT of time on consumption in general. While this may make me good as a judge of comparing different media types for others to better know what they should spend their scarce time upon, it does highlight the sheer percentage of time I dedicate to items that most people think is (mostly) a waste of time.

Honestly, I do not mind others making this judgment. It's a judgment I sometimes think I agree with. But, overall, I'm fairly happy with my current level of consumption. While I might change these habits in the future, I would require an equal level of intellectual stimulation on a broad range of topics to really make up for the content I now consume everyday. I might be committed to the cause of optimal philanthropy, but focusing on only one area is just not something that I ever think I could do while maintaining my current levels of happiness. That's why I fully expect to continue to consume such a large amount of content like this on a regular basis.

Edit: Commenters have brought two additional philosophy podcasts to my attention: Public Ethics Radio and The Thirst. I've yet to listen to them, but they appear interesting.

On Ada Lovelace day, bloggers generally write about a woman in the field of science, technology, engineering, or mathematics. It's relevant because even today, in 2012, we have far, far too few female STEM professionals. I'm not sure if the reason has anything to do with people thinking women can't succeed as well in these fields, but if so, it makes sense to celebrate feminist scientists on at least one day each year. And today is that day.

This study is perhaps the most depressing study on sexism in science academia I have ever read. It is so distressing that upon first encountering it, I thought that it was surely wrong, and that a quick glance through their methodology would show why their findings were wrong. But, after careful consideration, I have to admit that this study is completely legit. I couldn't find even a single flaw in their approach.

As Scientific American reports, this study has conclusively proven that significant gender bias exists in science academia. They used a double-blind randomized controlled experiment -- and when I say, controlled, I mean controlled. They even made sure that the names used (John & Jennifer) were pretested as equivalent in likeability and recognizability. They covered every conceivable base. And the results are horrifying.

They created a single fake resume/application that was good enough to warrant a hire, but not so good as to necessitate it (as established in a prestudy). They then sent this application to 127 science faculty as though it were real. (After the study was done, they went back and asked these people if they suspected it was fake; none did.) The 127 faculty chosen had demographics corresponding to both the averages for the selected departments and faculty at all United States research-intensive institutions, meeting the criteria for generalizability even from nonrandom samples. Not only was their sample representative of the underlying population, but they specifically chose 127 as the optimal sample size needed to detect effects without biasing results toward obtaining signiﬁcance.

These 127 science faculty judged the applications on competence, hireability, and whether they would offer to mentor the applicant. Males were significantly preferred over females on all metrics. Furthermore, the faculty were asked to estimate what salary would be appropriate for the successful applicant. Males were offered far higher salaries.

The sexism in today's science academia is real. While this doesn't mean that science faculty are overtly sexist, nor even consciously sexist, there is a distinct significant privilege that exists for male newcomers to science academia.

So today, on Ada Lovelace Day, when you read stories of female success stories in science across the web, realize just how hard it was for those standouts to achieve what they did. Even in today's world, being female in science is tough.

EDIT: After writing this article, commenters pointed out problems with the graphs used. In particular, satt pointed out that the use of dynamite plots here is possibly misleading, and unnecessarily obfuscates the actual data points at best.

Unfortunately, the charts were taken directly from the original paper, and so I do not have access to the actual data needed to create better plots for this article review. I have e-mailed the lead author, Corinne A. Moss-Racusin, to see if they have any violin plots with better axes that they could use to alleviate these concerns.

14 October, 2012

Each year, I try to write a post for Blog Action Day that gets to the heart of the topic. This year is no different.

The theme this time around is The Power of We, and most people are discussing just how much power we collectively have toward accomplishing social good. However, I want to focus on something that most altruists seem to ignore: the massive potential power that we miss out on when donating to the wrong causes.

Not all nonprofits are equally good at effecting positive change. The differential in outcomes created between two random charities is likely several orders of magnitude. This is why it is so important to analyze which charitable cause is more capable of turning your donated dollar into additional social good. Thankfully, there are a few organizations that do this analyzation work for you.

GiveWell does an extraordinary job of ranking highly effective charities by how confident we can be that donating to them will result in good outcomes. Unfortunately, it only does well with ranking certain types of charities; specifically, it only ranks those charities that are already known to be highly effective (they do a good job of distinguishing #1 from #2, but not #10 from #11, if you're interested in knowing that kind of thing), and when a charitable need is not served well by any particular charity, it fails to give recommendations for that field, even if the (bad) charities in that field might result in higher potential gains. (The field of existential risk, for example, has no recommended charities.) Further, it focuses on being able to match small incremental gains with additional funding and so misses out on identifying larger gains accomplished that can't be verified step-wise. In other words, GiveWell places a high priority on knowing that their recommendation is accurate, and refuses to recommend charities which potentially are effective but which have so far not been proven as such.

For all these qualifiers, GiveWell ends up doing extremely well at what it means to do. Although it is missing out on some potential giving opportunities which might be more effective, you can always feel confident that if GiveWell recommends a charity, then that means there is reason for very high confidence that donating to them will accomplish serious social good.

An alternative to GiveWell's recommendation is Giving What We Can. Unlike GiveWell, which attempts to provide highly effective donation choices in a variety of fields (on the assumption that donors are more likely to give to projects which perform well in a field they're interested in), Giving What We Can has much more of a bottom line approach. GWWC breaks things down to the bare utilons and determines a sheer top recommendations list, so that donors can truly maximize good overall rather than in a specific field.

Lastly, there are two major fields where GiveWell does not give out recommendations, yet these fields might be some of the most effective ways of achieving good through donations. The first is existential risk, which GiveWell is currently working on; the second is animal welfare, which GiveWell explicitly stays away from. While no organization is currently fit to be rated highly in terms of existential risk, charities which focus on taking the moral status of animals seriously can be examined through Effective Animal Activism. While they do not rank animal charities against human-focused ones, they do a good job of determining which animal welfare oriented charities accomplish the most good per dollar donated.

Analyzing the effectiveness of nonprofits is not easy; there is far more subtlety involved than you might at first think. This is why I highly recommend going to one of the above sites before making any large giving decisions. If we want to maximize the power of we, we first must maximize the amount of good we accomplish with each dollar we donate.

Goodreads

This story is hard science fiction at its best. I thoroughly enjoyed this book not only for its exploration of plausible yet utterly fantastic ideas, but also for the story and characterization as well. Like all hard scifi, the main focu...

This book is hard science fiction at its best. I found myself riveted by each new section, unable to put the book down for more than thirty seconds at a time. The combination of a compelling story with such scientifically plausible eleme...

Although some sections suffer from the prejudices of the day, overall this book really touched my heart. I found myself really enjoying all the characters in their own way, and I loved the way that Anne changed over the course of her yea...

Although the book suffers from the blatant sexism of its day, it was forward thinking for its time, and had some very positive messages about what ideals should be truly valued. The science in the book was hit or miss; some parts make it...